Question: What do the following two equations represent? $x+2y = 1$ $-6x+3y = -4$
Answer: Putting the first equation in $y = mx + b$ form gives: $x+2y = 1$ $2y = -x+1$ $y = -\dfrac{1}{2}x + \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $-6x+3y = -4$ $3y = 6x-4$ $y = 2x - \dfrac{4}{3}$ The slopes are negative inverses of each other, so the lines are perpendicular.